French elite forces stormed two hostage sites Friday, killing two brothers behind the Charlie Hebdo massacre and a third jihadist ally in a fiery end that also claimed the lives of four hostages.

The killings brought a dramatic end to three days of terror and high tension that began Wednesday when the heavily armed Kouachi brothers burst into the satirical magazine's office and slaughtered some of France's best-loved cartoonists.

As shots and explosions rang out in the City of Light, five people, including the gunman, were found dead in the aftermath of the assault on a Jewish supermarket in eastern Paris and several captives were freed, security sources said.

Gunmen at both sieges told French TV they were acting together in the name of al-Qaeda in Yemen and the Islamic State group.

Seven people, including three police, were hurt in the supermarket raid with officers carrying some of the terrified hostages clear from the scene in their arms.

"It's war!" screamed a mother as she pulled her daughter away.

An AFP reporter saw at least one body lying at the scene, where the sliding glass door of the shop was completely shattered.

The dramatic climax to the two standoffs brought to an end 53 hours of terror that began when the two brothers slaughtered 12 people at satirical magazine Charlie Hebdo in the bloodiest attack on French soil in half a century.

The weekly had lampooned jihadists and repeatedly published cartoons of the Prophet Mohammed which angered many Muslims.

After the three days of bloodshed, France was mourning the loss of 17 people and tending to 20 injured.

Supermarket gunman Amedy Coulibaly told French TV he was a member of the Islamic State extremist group and had coordinated his atrocities with one of the Charlie Hebdo gunmen, Cherif Kouachi, who told television he was backed and financed by al-Qaeda in Yemen.

In a telling detail, revealed by BFMTV, the supermarket attacker did not hang up the phone properly after talking to its reporters, allowing the police to overhear him.

And it was as he knelt to do his evening prayer that they stormed the building.

President Francois Hollande said after the sieges had ended, the threats facing France "weren't over."

He described the attack on the Jewish supermarket as an "appalling anti-Semitic act" and said: "these fanatics have nothing to do with the Muslim religion."

Hollande said he would attend a march of national unity on Sunday that is expected to draw hundreds of thousands including the leaders of Germany, Italy and Britain.

About 30 kilometres (16 miles) to the northeast, in the small town of Dammartin-en-Goele, the two Islamist Charlie Hebdo gunmen staged a desperate escape bid, charging out of the building all guns blazing at the security forces before being cut down in their tracks, a security source said.

Police confirmed their identity as Cherif and Said Kouachi, French-born orphans of Algerian origin.

The other hostage-taker in the eastern Porte de Vincennes area of Paris was also suspected of gunning down a policewoman in southern Paris Thursday.

French police released mugshots of Coulibaly, 32, as well as a woman named as 26-year-old Hayat Boumeddiene, also wanted over the shooting of the policewoman.

The Vincennes area was swamped with police who shut down the city's ringroad as well as schools and shops in the area. Authorities ordered residents to stay indoors.

In Dammartin-en-Goele, only 12 kilometres (seven miles) from Paris's main Charles de Gaulle airport, French elite forces had deployed snipers on roofs and helicopters buzzed low over the small printing business where the Charlie Hebdo suspects had been cornered early Friday.

Ahead of the stand-off, police had already exchanged fire with the pair in a high-speed car chase.

One witness described coming face-to-face at the printer's with one of the suspects, dressed in black, wearing a bullet-proof vest and carrying what looked like a Kalashnikov.

The salesman told France Info radio that one of the brothers said: "'Leave, we don't kill civilians anyhow'."

One 60-year-old choked back tears as she said how elite forces burst into the shop where her daughter works and ordered them to take cover.

Prior to the standoff, the suspects had hijacked a car from a woman who said she recognised the brothers.

The spectacular attacks came as it emerged the brothers had been on a US terror watch list "for years".

And as fears spread in the wake of the attack, the head of Britain's domestic spy agency MI5 warned that Islamist militants were planning other "mass casualty attacks against the West" and that intelligence services may be powerless to stop them.

Wednesday's bloodbath at Charlie Hebdo, which had repeatedly lampooned the Prophet Mohammed, has sparked a global chorus of outrage, with impromptu and poignant rallies around the world in support of press freedom under the banner "jesuischarlie" (I am Charlie).

US President Barack Obama was the latest to sign a book of condolence in Washington with the message "Vive la France!" as thousands gathered in Paris on a day of national mourning Thursday, and the Eiffel Tower dimmed its lights to honour the dead.

And as a politically divided and crisis-hit France sought to pull together in the wake of the tragedy, the head of the country's Muslim community -- the largest in Europe -- urged imams to condemn terrorism at Friday prayers.

In a highly unusual step, Hollande met far-right leader Marine Le Pen at the Elysee Palace on Friday, as France geared up for a "Republican march" on Sunday expected to draw hundreds of thousands including British Prime Minister David Cameron and his Spanish counterpart Mariano Rajoy and Italy's Matteo Renzi.

Interior Minister Bernard Cazeneuve announced that a total of 88,000 security forces were mobilised across the country and that an international meeting on terrorism would take place in Paris on Sunday.

Nine people had already been detained as part of the operation, Cazeneuve said.

Meanwhile, questions mounted as to how a pair well-known for jihadist views could have slipped through the net and attack Charlie Hebdo.

Cherif Kouachi, 32, was a known jihadist convicted in 2008 for involvement in a network sending fighters to Iraq.

Said, 34, has been "formally identified" as the main attacker in Wednesday's bloodbath.

A senior US administration official told AFP that one of the two brothers was believed to have trained with Al-Qaeda in Yemen, while another source said that the pair had been on a US terror watch list "for years".

The brothers were both flagged in a US database as terror suspects, and also on the no-fly list, meaning they were barred from flying into the United States, the officials said.

The Islamic State group's radio praised them as "heroes" and Somalia's Shebab militants, Al-Qaeda's main affiliate in Africa, hailed the massacre as a "heroic" act.

Refusing to be cowed, the controversial magazine plans a print run of one million copies instead of its usual 60,000, as journalists from all over the French media landscape piled in to help out the decimated staff.

"It's very hard. We are all suffering, with grief, with fear, but we will do it anyway because stupidity will not win," said columnist Patrick Pelloux.